# A fly in the train kinda question ;)

## Main Question or Discussion Point

So, this is pretty basic, but unfortunately I'm not sure of the answer -

A fly is flying in a train, in the air, but isn't moving (one of these static-annoying flies). Then the train starts moving. The fly would then be seen to people sitting on the seats as though moving towards the back of the train, right?

Then I thought - ok, the same thing has to happen with air molecules.
But then - how come we don't feel "wind" when the train starts moving?
Worse then that - how come we don't feel wind with the earth rotating around itself as rapidly as it does?

Made me think I need to restudy Mechanics :-)

Thanks a lot.
Tomer.

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When the train is at rest the molecules move randomly and we don't feel any wind. As the train starts moving forward, the back wall advances and hits the molecules, sending them in the same direction the train is moving. That's why we don't feel any wind even though the train is moving.

xts
It is not a question about mechanics, but about insect's behavioural psychology.

The fly keeps her position dynamically: adjusting wind flapping such, to keep her position fixed regarding several points she'd chosen as a reference. Most probably those points are in the wagon rather than outside the window. So as the train starts, the fly keeps her position relative to the wagon.

Fly's innertia is marginal in this process.

The same process (but not so intelligently as regarding insects) applies to air molecules. They fly in all directions, but are distributed uniformly in the wagon. They "fix" this distribution by equilibrium between bouncing from left and right wall. The air inertia is negligible (not sufficient to feel a wind) comparing to dynamical balance between particles and the walls.

russ_watters
Mentor
Then I thought - ok, the same thing has to happen with air molecules.
But then - how come we don't feel "wind" when the train starts moving?
The air moves with the train. It kinda has to, doesn't it? Where else would it go? There isn't anywhere near enough acceleration for the air's own mass to cause it to noticeably pile up at the back of the train.
Worse then that - how come we don't feel wind with the earth rotating around itself as rapidly as it does?
The atmosphere rotates with the earth, at roughly the same speed. Why? There's nothing to stop it. Or looking at it the other way: if the atmosphere didn't rotate with the earth, aerodynamic drag would quickly make it rotate with the earth.

BruceW
Homework Helper
Then I thought - ok, the same thing has to happen with air molecules.
But then - how come we don't feel "wind" when the train starts moving?
Worse then that - how come we don't feel wind with the earth rotating around itself as rapidly as it does?
Very good question. The air is an ideal fluid. Therefore the pressure is the same in all directions. Think about it - gravity is acting down on the air, so you might think that the pressure from the air would act more in a downwards direction. But actually the pressure on us from the air is the same in all directions.

So when the train accelerates, we don't feel any extra pressure from the air because it is an ideal fluid.

About the earth's rotation - there are several phenomena that manifest due to the non-inertial motion of the earth's surface. Try wikipedia maybe.

Thank you all for your answers. I kinda told myself something about pressures taking care of it all, but I wasn't sure and wanted approval :-)

Tomer.

Ken G
Gold Member
Just to follow up, the key comparison is between the acceleration a of the train during a sound crossing time in the air, and the sound speed in the air v. The mass of the air doesn't seem to be the issue, except insofar as it affects the sound speed. The sound crossing time is L/v, where L is the size of the compartment, so we are comparing aL/v to v, so aL to v2. As long as the first number is much smaller, the air will move with the train, and the fly with the air. If the first number is larger, the air will "pile up" and generate large pressure gradients and winds inside the compartment, and the fly will lag toward the back of the train.

But why does the fly move with the air? I'm thinking of the fly as being fixed to a point on earth (or to the train station maybe) rather than the train. Like, let's say he flies like a geostationary satellite and then falls asleep :-). When the train then starts moving, will he "move with the air" forwards? Won't he be dragged backwards?

It might be stupid to insist of the fly, but a friend of mine ask me that, and I pretty much told him that the fly would move backwards if he's not resting at first on some seat of the train/catching up with the train, but then the air issue bothered me. So the air resolution I understand better now (kind of), but now I'm confused again about the fly :)

If the train was full of water instead of air then the fly would certainly move forward.
But because air is much less dense, when the train starts from a stationary position and begins to move forward the drag force working against the fly to put it in motion will be much less.

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xts
Flies mantain ther position dynamically - they used to do so in changing wind. They have no GPS nor efficient accelerometer (ear labirynth we - mammals - use is a very precise tool, comparing to insects) - so they can't be 'an inert satellite'. They use their eyes to maintain position relative to neighbouring objects. You may try it - as such annoying fly hovers neer your nose - move your head slowly - it is likely the fly will follow your nose...
In a train the fly maintains her position relative to some reference points she'd chosen from details of cart interior.

Flies mantain ther position dynamically - they used to do so in changing wind. They have no GPS nor efficient accelerometer (ear labirynth we - mammals - use is a very precise tool, comparing to insects) - so they can't be 'an inert satellite'. They use their eyes to maintain position relative to neighbouring objects. You may try it - as such annoying fly hovers neer your nose - move your head slowly - it is likely the fly will follow your nose...
In a train the fly maintains her position relative to some reference points she'd chosen from details of cart interior.
That's interesting, but I guess I used the fly just because I wanted something floating that's disconnected from the train, and yet big enough so that we could see it and intuitively speak about it. :-) It could be a genius fly, with a built-in GPS system, as far as I'm concerned :-)

Anyway, I think it's all clear now. Thanks again everyone.

A.T.
Flies mantain ther position dynamically - they used to do so in changing wind. They have no GPS nor efficient accelerometer (ear labirynth we - mammals - use is a very precise tool, comparing to insects) - so they can't be 'an inert satellite'. They use their eyes to maintain position relative to neighbouring objects.
Hovering in a train in nothing compared to hovering in rain:

Hovering in a train in nothing compared to hovering in rain:

I'll... remember that :-)

xts
I wanted something floating that's disconnected from the train, and yet big enough so that we could see it and intuitively speak about it. :-) It could be a genius fly, with a built-in GPS system
Better take a pendulum made of a (really dumb) lead ball 10g or so hung on a half metre long thread tied to a carriage shelf - that will work as you expected.

Perhaps it would be interesting for you to think about what would happen to a helium filled balloon (that floats) in an accelerating train/car. You may wish to think about this for a bit. Keep in mind the balloon floats as it is lighter than air.

The result is the balloon moves in the same direction as the acceleration. Remember that acceleration is really indistinguishable from gravity. Therefore, in a situation where you are accelerating forward, this will cause the same type of movements as if gravity was pulling from the back.

The balloon only moves forward because it is lighter than air. If it were heavier than air (as most things are) it would move backward. If it were exactly neutrally buoyant (exact same weight as air of the same volume), it would float where ever it was placed and would not move at all even during acceleration (relative to people inside the car).

If you buy a mylar party balloon (which you can buy prefilled at dollar stores), and wait a few days for it to lose helium, it will eventually achieve nearly neutral buoyancy. I've always found balloon at that point quite interesting to play with. You could test its behavior in a car yourself (both when it floats and then a few days later when it is neutral).

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Very interesting video, thanks!!
It is remarkable and astonishing to see such simple principles looking suddenly like science fiction ;)

BruceW
Homework Helper
I guess there's two main effects going on:
1) The acceleration of the car causing a non-inertial reference frame. So, ignoring the air in the car for a moment, any object will accelerate backwards (in the car's reference frame).
2) If the car has air in it (which most do), the air will now experience an acceleration toward the back of the car. If we assume the air forms an equilibrium state with itself, then there will be a pressure gradient similar to the one caused by gravity. So the pressure at the back of the car will be greater than the pressure at the front of the car.

These two effects will combine so that if the density of the object is greater than that of the air, the object will move towards the back of the car, but if the density of the object is less than that of the air, the object will move towards the front of the car.
And for objects whose density is much greater than that of the air, the acceleration towards the back of the car is simply equal to the acceleration of the car.

Also, interestingly, if we have an object whose density is equal to that of the air. (For example a balloon which would hover still in mid-air). Then if the car accelerates forward, the balloon will maintain its position in the car's frame of reference! In other words, if you put the balloon in the air next to you while you drive, it will stay in exactly the same place! No matter how dangerously you took the corners! (I'm not advising you try this at home).

Edit: Actually, since I assumed that the air is in equilibrium with itself, these conclusions might not be true when the acceleration of the car is rapidly changing. So let me change that last point about the balloon hovering still next to you in the car: If you start turning a corner, then put the balloon there while continuing to turn the corner, the balloon won't move. (In other words, it shouldn't move while the car is under constant acceleration).

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